Algebraically Accurate Volume Registration Using Euler's Theorem and the 3-D Pseudo-Polar FFT

• Authors: Yosi Keller;Amir Averbuch;Yoel Shkolnisky
• Venue: CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
• Year: 2005

We present an algorithm for the registration of rotated and translated volumes, which operates in the frequency domain. The Fourier domain allows to compute the rotation and translation parameters separately, thus reducing a problem with six degrees of freedom to two problems of three degrees of freedom each. We propose a three-step procedure. The first step estimates the rotation axis. The second computes the planar rotation relative to the rotation axis, and the third recovers the translational displacement by using the phase correlation technique. The rotation estimation is based on Eulerýs theorem, which allows to represent a rotation using only three parameters. Two parameters represent the rotation axis and one parameter represents the planar rotation perpendicular to the axis. By using the3-D pseudo-polar FFT, the estimation of the rotation axis is shown to be algebraically accurate. A variant of the angular difference function registration algorithm is derived for the estimation of the planar rotation around the axis. The experimental results show that the algorithm is accurate and robust to noise.